In the virtual presence of a heavy quark t, the interactions of a
CP-odd scalar boson A, with mass M_A « 2M_t, with gluons and
light quarks can be described by an effective Lagrangian. We
analytically derive the coefficient functions of the respective
physical operators to three loops in quantum chromodynamics (QCD),
adopting the modified minimal-subtraction (MS-bar) scheme of
dimensional regularization. Special attention is paid to the
proper treatment of the gamma_5 matrix and the Levi-Civita epsilon
tensor in D dimensions. In the case of the effective ggA coupling,
we find agreement with an all-order prediction based on a
low-energy theorem in connection with the Adler-Bardeen
non-renormalization theorem. This effective Lagrangian allows us
to analytically evaluate the next-to-leading QCD correction to the
A → gg partial decay width by considering massless diagrams. For
M_A = 100GeV, the resulting correction factor reads
1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx
1+0.68+0.23. We compare this result with predictions based on
various scale-optimization methods.